A machining apparatus for machining rotationally driven workpieces with Y-axis movement are known in the prior art. US 2010/0202847 shows a machining apparatus having a vertical main spindle, tool turret, and a hobber. The machining units are mounted on the front vertical wall of the machine frame. The tool turret and the hobber can be moved vertically and horizontally on a compound slide. In addition, the hobbing spindle includes a swivel axis (B axis) and a shift axis, and can furthermore be moved in a third axis (Y axis). Guides in the direction of the Y axis are mounted in front of the vertical wall of the machine frame. This necessarily results in a relatively large distance between the rotation axes and the frame wall, which distance negatively affects the flow of power and machine rigidity.